Application of Eigenfunction Orthogonalities to Vibration Problems

The modelling of vibration problems is of great importance in engineering. A popular method of analysing such problems is the variational method. The simplest vibration model is represented using the example of a long rod. Two kinds of eigenfunctions orthogonality are proved and the corresponding norms are used to derive Green's function that gives rise to an analytical solution of the problem. The method can be easily generalized to a broad class of hyperbolic problems.